The Effects of Demand Referral on the Inventory Levels in Multi-channel Distribution Systems Hainan Li
Yibin Li
School of Management Huazhong University of Science & Technology E-mail:
[email protected]
School of Management Huazhong University of Science & Technology
Abstract—In a setting a supplier selling directly to the end customers by her wholly-owned Internet online channel, as well as a traditional physical retail channel, the supplier may refer her customers to the retailer (demand referral) when out of stock where the supplier stocks only for the online customers. The retailer pays for the excess demand of the supplier and the excess customers have a substitution rate to the retailer. We explore the impact of the demand referral (DR) on the multi-channel distribution systems. The results show that when the price of DR is predetermined by negotiation the use of DR increases the base-stock level of the retailer but decreases the base-stock level of supplier in competitive setting. Therefore, DR improves the efficiency of the global supply chain compared with understock of the retailer in traditional supply chain. Finally, numerical experiment is used to illustrate the results of this paper.
used to direct their customer demand to traditional retailers, and thus outsource the demand fulfillment process to traditional retailers [3].
Index Terms—Supply chain management; multi-channel distribution; Electronic Commerce; Inventory management; Demand referral
I.
Introduction
Consider such a supply chain in which a supplier selling directly to the end customers by her wholly-owned Internet online channel as well as a traditional physical retail channel. The supplier in the supply system simultaneously acts as a competitor to the retailer. In such multi-channel distribution systems (MCDS), customers with different preference to shopping channel may choose the most preferred one to meet their demand. However, when the seller of one channel selected first is out of stock, the customer may transfer to other one seller or even the other channel as a second choice, wait in the same channel to the next period, or quit. In a periodic replenishment system facing demand uncertainty, the supplier and the retailer may cooperate to fulfill the excess demand from either player who is out of stock to reduce the loss, where some ways to cooperate may be used including drop-shipping [1][2], demand referral [3] et al. The interest of this study is the latter. Demand referral (DR), emerging in some firms such as 1800-Flowers.com, Amazon.com, is an approach that e-tailer
In MCDS, when the stock for online demand is used up, the supplier may refer her customers to the retailer who pays a price for the excess demand. Thus, a part of the excess demand who would like to select the retailer as the second choice will stay to be met in the retailer and the rest is lost in the same period. So, DR retains a part of unmet demand in the supplier, therefore increases profit of the whole system. The remainder of the paper proceeds as follows. In Section 2, we review the relevant literature. In Section 3, we detail our model and notation. In Sections 4, we conclude and future research.
II.
Literature Review
There are mainly two types of literature related to our topic: DR and inventory allocation related to demand substitution in different distribution channels. As we known, Reference [3] is the only academic literature talked about DR. In the fourth part of zheng’s dissertation issues on multi-channel supply chains for doctorate degree of Duke University, DR is viewed as an approach to horizontally cooperate in e-fulfillment process, in which e-tailer makes additional marketing effort to customer acquisition and refers the demand acquired to traditional retailers who incurs a penalty cost. The author believes that application of DR to competitive scenario induces the separation of the marketing and operations functions resulting in inefficiencies, and analyses validity of some inventory allocation policies in the setting. Papers on inventory allocation related to demand substitution are as follows. Van Ryzin and Mahajan [4] investigate inventory decisions when horizontal competing among either manufactures or retailers in one of the echelons with demand substitution and present some coordination mechanisms. Smith and Agrawal [5] explore management of multi-item retail inventory systems with demand substitution. Netessine and Rudi [6] present centralized and competitive inventory models with demand substitution and believe that
when demand is multivariate normal the total profit of centralized system is decreasing in demand correlation. Reference [7] explores problems of competitive stocking and coordination in a multiple-channel distribution system, indicates the channel inefficiencies induced by the presence of simultaneous vertical competition and horizontal competition (price double-marginalization and substitution between channels exist simultaneously), and believes that an appropriately designed but hard implemented penalty contract or a two-part compensation-commission contract can coordinate the supply chain in which the latter depends on the retail channel sales. Zheng [3] explores the DR supply chain from the perspective of marketing management compared with dropshipping supply chain and highlights the effects of supplier’s marketing effort not DR operations itself on inventory level in MCDS. Under a drop-shipping arrangement, the retailer serves as a middleman who acquires customers and accepts orders while the wholesaler owns and holds inventory and also fulfills orders [1]. The second type of literature explores inventory management or coordination mechanisms with substitution originated from demand diversity between products or channels in which the substitution is bilateral. Different from the literature mentioned above, this paper focuses on the effects DR on the inventory levels in MCDS in which the substitution is unilateral from a supplier to retailers when the supplier is out of stock. Another difference is that we analyze the effect the price of DR on levels of competitive base stock in MCDS.
III.
Model and Notation
A schematic representation of the MCD system with the supplier adopting DR is provided in Fig.1. This is different from [7].
the product from the manufacturer at a unit wholesale price w and sells it at a price pr . We assume that all prices are exogenous and
c < ps and c < w < pr . We also assume that each channel has a limited local monopoly because of channel differentiation. So, the total market demand is shared by two channels. Let
Dx and
~
Dy
respectively denote the “first-choice” demand faced by supplier online channel and the retail channel in a period. In case of a stock out at supplier online channel a fraction α of the customers whose first-choice is the supplier online channel will search the product at the retail channel. To understand the effects of DR on the inventory levels, we assume that no customer whose first-choice is the retail channel will search the product at the supplier channel in case of a stock out at the retail channel. In the event that the product is out of stock at the both channels, we assume that the demand will be lost and no
D
after effects of lost customer demands. In fact, x is also the all demand faced by the supplier in the same period because no demand from other channel. For analytical tractability, we ~
Dx D y
assume that the demand profile ( , ) follows a known, continuous joint distribution, with a corresponding set of marginal strictly increasing cdf. Analogous to the Boyaci (2005), we assume that the demands across different periods are independent and identically distributed. Under an undiscounted, infinite-horizon, average profit maximization criterion, We model a supply chain in which excess demand (after substitution) is lost, replenishment leadtimes are zero, and supplier has infinite supply capacity at the upper echelon. Consequently, the supplier does not hold any stock at this level; stocks are kept by the supplier and the retail channels only to satisfy end-customer demands. At the beginning of one period, the price of DR is predetermined by negotiation, denoted τ ; unmet demand referred from supplier cost the retailer the same τ . Let D y denote the “composite” single-period demand for the retail channel that includes the first-choice customers as well as any spill-over customers substituting the product. Then ~
D y ＝ D y + α ( Dx − x) + D
There is a single supplier (manufacturer or wholesaler perhaps) whose product has a unit cost c , distributed by her wholly-owned online sales channel (i.e. “supplier online channel” with e-tailer) and an independent retail channel (i.e. “retail channel” with retailer). The product is sold in the supplier online channel at a price
ps
. The retailer purchases
and recall that x is also the all demand faced by the supplier in the same period. The retailer’s expected profit is + π r ( x, y ) ＝ ( pr − w) y − τ E ( D x − x )
− ( p r − w + hr ) E ( y − D y ) +
(1)
and the supplier’s expected profit is
π s ( x , y ) ＝ ( p s − c) x − ( ps − c + hs )E( x − Dx ) +
The supplier has a unique best response base-stock level
y ( x) given by: x( y ) = ⎧⎪ p s − w − τ − ( w − c)αP( D y ≤ y * , Dx > x * ) ⎫⎪ : ( ) x P D x ≤ = ⎬ ⎨ x p s − w − τ + hs ⎪⎭ ⎪⎩ （7）
+ ( w − c)[ y − E ( y − D y ) + ]
+ τE ( D x − x ) +
(2)
where the wholesale price per unit is denoted w , the holding cost per unit of retail and supplier online channel
hr and
hs respectively. The supply chain profit π c is the sum of the supplier and the retailer profits and is independent of the wholesale price and the demand referral price:
Let ( x , y ) denote the equilibrium base-stock levels of the supplier and the retailer respectively. When the two players set a fixed τ by negotiation, the Nash equilibrium is characterized as the fixed point of the best response functions of (6) and (7).
D
π sc ( x , y ) = ( ps − c) x − ( ps − c + hs ) E( x − Dx )
^
^
Proposition 1. If
p s − w − τ > ( w − c)α
+
+ ( pr − c) y − ( p r − c + h r ) E ( y − D y ) + . (3)
^
^
Proposition 2. For a fixed wholesale price w and a fixed ^
demand referral price
(4)
P ( Dx ≤ x * )
^
decreases x .
^
^
(5)
y*
Where x , denote the optimal inventory levels of supplier online and retail channel respectively. From (4) and (5), we conclude that when the price of demand referral is predetermined as fixed, DR has no effect on the optimal inventory levels of supplier online and retail channel in centralized setting.
B. In competitive setting The retailer has a unique best response base-stock level
y ( x) given by: ⎧ pr − w ⎫ y(x) = ⎨ y : P(Dy ≤ y) = ⎬ pr − w + hr ⎭ ⎩
α , an increase in τ
decreases x but increases y , and increases .
αm = α
and α r = 0 , the proofs of which are presented). From (1), (2), (7) and the submodularity of the profit functions, we get the following proposition 3. Proposition 3. For a fixed w and
p s − c − ( pr − c + hr )αP( D y ≤ y * , Dx > x * )
*
τ , an increase in α increases y and
The two propositions are analogous to [7] (just let
pr − c P( D y ≤ y * ) = pr − c + hr
the
From the proposition, the equilibrium of inventory competition game is influenced by the price of demand referral.
and Rudi, 2003] can be stated as:
ps − c + hs
then
equilibrium ( x , y ).
We assume that
=
holds,
inventory competition game has a unique, globally stable Nash
A. In centralized setting
( ps − c + hs ) > α ( pr − c + hr ) , then π r ( x, y ) , π s ( x, y) and π sc ( x , y ) are submodular in ( x, y ) . Consequently, the optimality conditions [Netessine
pr − w pr − w + hr
πr . α
For a fixed w , an increase in
πs
but decreases
τ and an decrease in
^
decrease x .
IV.
NUMERICAL EXPERIMENT
To illustrate the results of the paper, we use the following numerical experiment. A. In centralized setting Both Dx and D y are assumed to be normal with mean μ =5 and standard deviation σ =1. The retail prices are fixed at ps = pr =5, and the unit product cost c =0. This suggests the optimal stock levels of the both channels are identical when
(6)
α = 0 in the centralized setting, and both the channels have identical holding costs, hs = hr =1.
Fig.5 The equilibrium profits of supplier online and retail channel as functions of the price of demand referral. Fig.2 Base-stock level of supplier online channel as a function of substitution rate to retail channel under centralized setting.
CONCLUSION
Focusing on e-fulfillment, contrary to direction of dropshipping operations, demand referral from supplier online channel to the retailer increases is a new trend in multi-channel distribution systems in era of e-commerce. In this paper, we have analyzed the effects of demand referral on competitive inventory levels and demonstrated that demand referral is beneficial to increase base-stock level of the retail channel and to decrease that of the supplier online channel, therefore effectively improving the service level in the multi-channel distribution systems.
B. In competitive setting
Fig.2 The equilibrium base-stock level of supplier online channel as a function of the price of demand referral and the substitution rate to retail channel. Let the substitution rate to retail channel values of parameters unchanged.
V.
α =0.5, and other
We show that when the price of demand referral is predetermined as fixed, DR has no effect on the optimal inventory levels of supplier online and retail channel in centralized setting. In competitive setting, the equilibrium of inventory competition game is influenced by the price of demand referral. We also show that the base-stock level of retail channel increases and the base-stock level of supplier online channel decreases in the price of demand referral. From these results, we have good ground to believe that demand referral reduces inefficiency of inventory and increases the profit of the global supply chain with an appropriate price of demand referral accepted by a competitive supplier and her retailer. However, the condition that the price of demand referral is predetermined as fixed is too strict. In fact, if the referred demand is unmet the retailer will incur a direct, out-of-pocket cost. Consequently, the price has something with the state of stock at the retail channel. To set the price of demand referral as a variable and to examine the effects of the dynamic price on the performance of the supply chain is worth to further investigate.
Fig.4 The equilibrium base-stock levels of supplier online and retail channel as functions of the price of demand referral.
Although the base-stock level of retail channel increases in the price of demand referral, it is impossible to set the price too high, that is to say, the stock level of retail channel is impossible to increase unlimited. Besides the price, some other factors should be considered. This is another worth investigation.
ACKNOWLEDGEMENT This research was supported by the National Natural Science Foundation of China under Grant 70332001.
REFERENCES [1] S. Netessine and N. Rudi, “Supply chain choice on the Internet,” Management Science, Vol.52, pp.844-864, June 2006. [2] M. Khouja and A. C. Stylianou, “A (Q, R) inventory model with a drop-shipping option for e-business,” Omega (2008), doi:10.1016/j.omega.2008.07.002. [3] X. Zheng, “Issues on multi-channel supply chains,” Doctorate Dissertation, Duke University, pp.118-153, 2005.
[4] G. Van Ryzin and S. Mahajan, “Supply chain coordination under horizontal competition,” Working paper, Graduate School of Business, Columbia University, New York, NY, 2000. [5] S. A. Smith and N. Agrawal, “Management of multi-item retail inventory systems with demand subsitution,” Operations Research, Vol.48, pp.50-64, Jan/Feb 2000. [6] S. Netessine and N. Rudi, “Centralized and competitive inventory models with demand substitution,” Operations Research, Vol.51, pp.329-336, Mar/Apr 2003. [7] T. Boyaci, “Competitive stocking and coordination in a multiple-channel distribution system,” IIE Transactions, Vol.37, pp.407-427, 2005.
